We know that the area of a rhombus can be calculated as:

where a and b are the lengths of the diagonals.
Then the area of the rhombus is:

Now, we also know that the area can be obtained by:

where s is the length of the side and h is the height. To obatain the height we need the length of the side. Then lenght of a rhombus is given by:
![s=\sqrt[]{((a)/(2))^2+((b)/(2))^2}](https://img.qammunity.org/2023/formulas/mathematics/college/5tv8haoo177z6pz877090gp4wjwcqgmqv2.png)
Then ins this case we have:
![\begin{gathered} s=\sqrt[]{((40)/(2))^2+((30)/(2))^2} \\ s=\sqrt[]{625} \\ s=25 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/oc7llnq8suv5hunrdrr9ij05f107627adv.png)
Now that we know the lenght of the side we use the second formula for the area to get h:

Therefore the height of the rhombus is 24 mm.